Review of Least Action Principle in Electromagnetics Part I: Derivation of Continuity Equation and Lorentz Force

Abstract

The paper deals with a derivation of equation of continuity for electric charge and Lorentz force. Starting from Hamilton's principle in classical mechanics and applying., gauge invariance one obtains Lagrangian for a moving charged particle. Equation of continuity and Lorentz force are obtained from the corresponding Lagrangian. The mathematical details of the functional minimization are given in Appendices.